I'm needing assistance with a 6th grade math problem (algebraic pattern equations). It's obviously popular as I've found the question on the web, but unfortunately, not the answer. Here goes:

Evelyn is reading about Windemere Castle in Scotland. Many years ago, when prisoners were held in various cells in the dungeon area, they began to dig passages connecting each cell to each of the other cells in the dungeon. If there were 20 cells in all, what is the fewest number of passages that had to be tunneled out over the years?

Evelyn is reading about Windemere Castle in Scotland.
Many years ago, when prisoners were held in various cells in the dungeon area,
they began to dig passages connecting each cell to each of the other cells in the dungeon.
If there were 20 cells in all, what is the fewest number of passages that had to be tunneled out over the years?

The only thing I know for sure is the answer is NOT 19.

Thanks so much!

Let's call the 20 cells: .

Consider cell
We can connect it to
There will be 19 passages.

Repeat this process for each of the cells.
There will be: passages.

But our list will have many duplicates.

. .

The passage from A to B is the same as the passage from B to A;
the passage from A to C is the same as the passage from C to A;. . and so on.